A026998 Triangular array T read by rows: T(n,k)=t(n,2k), t given by A027960, 0<=k<=n, n >= 0.

1, 1, 1, 1, 4, 1, 1, 4, 8, 1, 1, 4, 11, 13, 1, 1, 4, 11, 26, 19, 1, 1, 4, 11, 29, 54, 26, 1, 1, 4, 11, 29, 73, 101, 34, 1, 1, 4, 11, 29, 76, 171, 174, 43, 1, 1, 4, 11, 29, 76, 196, 370, 281, 53, 1, 1, 4, 11, 29, 76, 199, 487, 743, 431, 64, 1, 1, 4

Offset

0,5

Comments

Right-edge columns are polynomials approximating Lucas(2n+1).

Links

Table of n, a(n) for n=0..67.

Formula

T(n, k) = Lucas(2n+1) = A002878(n) for 2k<=n, otherwise the (2n-2k)th coefficient of the power series for (1+2x)/{(1-x-x^2)(1-x)^(2k-n)}.

Example

............................1
..........................1,1
........................1,4,1
......................1,4,8,1
..................1,4,11,13,1
...............1,4,11,26,19,1
............1,4,11,29,54,26,1
........1,4,11,29,73,101,34,1
....1,4,11,29,76,171,174,43,1
1,4,11,29,76,196,370,281,53,1

Crossrefs

This is a bisection of the "Lucas array" A027960, see A027011 for the other bisection.

Row sums are in A000918. Right-edge columns include A034856, A027966, A027968, A027970, A027972.

Sequence in context: A091570 A116669 A016523 * A326812 A324893 A301626

Adjacent sequences: A026995 A026996 A026997 * A026999 A027000 A027001

Keyword

nonn,tabl

Author

Clark Kimberling

Extensions

Edited by Ralf Stephan, May 05 2005

Status

approved